Question

. A two digit number is such that the product of its digits is 24. When 18 is
subtracted from this number, the digits interchange their places. Find the number.
​

Answer 1

A two digit number is such that the product of its digits is 24. When 18 issubtracted from this number, the digits interchange their places. Find the number.

$\underline{\textbf{Given:}}$

$\textsf{A two digit number is such that the product of}$

$\textsf{its digits is 24.}$

$\textsf{When 18 is subtracted from this number,}$

$\textsf{the digits interchange their places.}$

$\underline{\textbf{To find:}}$

$\textsf{The number}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the two digit number be 10x+y}$

$\textsf{Product of digits = 24}$

$\implies\mathsf{xy=24}$ --------------(1)

$\textsf{When 18 is subtracted,}$

$\mathsf{10x+y-18=10y+x}$

$\mathsf{9x-9y=18}$

$\mathsf{x-y=2}$

$\mathsf{x=y+2}$ -------------(2)

$\textsf{Using (2) in (1), we get}$

$\mathsf{(y+2)y=24}$

$\mathsf{y^2+2y-24=0}$

$\mathsf{(y+6)(y-4)=0}$

$\mathsf{y=-6,4}$

$\mathsf{But\;y\;cannot\;be\;negative\;\implies\;y=4}$

$\mathsf{when\;y=4,\;x=y+2}$

$\implies\mathsf{x=4+2}$

$\implies\mathsf{x=6}$

$\mathsf{Now,}$

$\mathsf{10x+y=10(6)+4=60+4=64}$

$\therefore\textbf{The required number is 64}$

Answer 2

Answer:

Step-by-step explanation: